I was asked about the possibility of using our $inner; instead of my $inner;. It's doable.

sub outer {
   ...
   local our $helper;
   $helper = sub {
      ...
      $helper->(...);
      ...
   };
   $helper->(@_);
}
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local still needs to be used to protect the current value of the variable and to clear the reference to the helper sub when outer exits.

I don't see any advantage in localizing $helper instead of &helper.